Finding the limit of a sequence

[dragoon7201]

the question gives {a_n} where a₁ = sqrt(3) and a_n+1 = sqrt(3 + a_n)
and assuming the sequence converges, what is the limit L that it converges to??

I am not sure how to start with this question, but I do know
Lim a_n = Lim a_n+1 since the sequence converges

 

[Ishuda]

the question gives {a_n} where a₁ = sqrt(3) and a_n+1 = sqrt(3 + a_n)
and assuming the sequence converges, what is the limit L that it converges to??

I am not sure how to start with this question, but I do know
Lim a_n = Lim a_n+1 since the sequence converges

If you know that, then let
a= Lim(a_n)
and, using some of the properties of limits,
\(\displaystyle a = \sqrt{3 + a}\)
How would you solve for a?

 

[dragoon7201]

Ohh I get it, cause lim a_n = L
so then lim a_n+1 = L = sqrt(3+L)
Thanks!